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A characterization of planar median graphs

100%

Peterin I.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

41-48

Median graphs have many interesting properties. One of them is-in connection with triangle free graphs-the recognition complexity. In general the complexity is not very fast, but if we restrict to the planar case the recognition complexity becomes linear. Despite this fact, there is no characterization of planar median graphs in the literature. Here an additional condition is introduced for the convex expansion procedure that characterizes planar median graphs.

Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations

75%

Pynko A. P.

Bulletin of the Section of Logic

2020

tom 49

nr 4

401-437

Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 𝔄4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable Sharing Property (VSP). We then characterize L4's having a theorem / inconsistent formula, satisfying VSP and being [inferentially] maximal / subclassical / maximally paraconsistent, in particular, algebraically through ℳ4|𝔄4's (not) having certain submatrices|subalebras. Likewise, [providing 𝔄4 is regular / has no three-element subalgebra] L4 has a proper consistent axiomatic extension if[f] ℳ4 has a proper paraconsistent / two-valued submatrix [in which case the logic of this submatrix is the only proper consistent axiomatic extension of L4 and is relatively axiomatized by the Excluded Middle law axiom]. As a generic tool (applicable, in particular, to both classically-negative and implicative expansions of DB4), we also prove that the lattice of axiomatic extensions of the logic of an implicative matrix ℳ with equality determinant is dual to the distributive lattice of lower cones of the set of all submatrices of ℳ with non-distinguished values.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 Discussiones Mathematicae Graph Theory

1 Peterin I.

1 Pynko A. P.

1 2020

1 2006

Wyniki wyszukiwania

A characterization of planar median graphs

Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations